Three kinds of extremal weight vectors fixed by a diagram automorphism
type: Item
instance of: scholarly article
title: Three kinds of extremal weight vectors fixed by a diagram automorphism
zbMATH Open document ID: 1030.17004
DOI: 10.1016/S0021-8693(03)00347-8
author: Satoshi Naito
author: Daisuke Sagaki
published in: Journal of Algebra
publication date: 2003-10-22T00:00:00Z
review text: A Dynkin diagram automorphism \(\omega\) induces a Lie algebra automorphism as well as an automorphism of the quantized universal enveloping algebra \(U_q(\mathfrak{g})\). The authors define an action of \(\omega\) on \(\tilde{U}_q(\mathfrak{g})\), the modified quantized universal enveloping algebra, introduced by \textit{G. Lusztig} in [Proc. Natl. Acad. Sci. USA 89, 8177-8179 (1992; Zbl 0760.17011)]. They consider a crystal base \(\mathcal B (\lambda)\) of an extremal weight module \(V(\lambda)\) and the subset \(\mathcal B^0 (\lambda)\) pointwise fixed by \(\omega\). They prove a canonical injection from \(\mathcal B^0 (\lambda)\) into the crystal base of a corresponding extremal module over the quantized universal enveloping algebra of the orbit Lie algebra.
reviewed by: Stefano Capparelli
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 1995434
zbMATH Keywords: crystals
zbMATH Keywords: quantized enveloping algebra
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1995434